Question

Eliminate $\theta$ from the equation $x=a\left(\sec \theta +\tan \theta \right);y=b\left(\sec \theta -\tan \theta \right)$

Answer 1

Give that:

$x=a(\sec \theta +\tan \theta )$ ......(1)

$y=b(\sec \theta -\tan \theta )$ ......(2)

Multiplying equation (1) and (2), we get

$xy=ab(\sec \theta -\tan \theta )(\sec \theta +\tan \theta )$

$xy=ab({\sec }^2\theta -{\tan }^2\theta )$

As we know that ${\sec }^2\theta -{\tan }^2\theta =1$

$xy=ab$

Or

$\frac{x}{a}=\frac{b}{y}$

Hence, this is the required solution.